ABUJA, Nigeria—When he appeared in a video on Monday boasting of having abducted more than 200 schoolgirls, the leader of terror group Boko Haram took the occasion to egg on the U.S. Army and get in a dig at ancient Egypt.

"We don't fear any American troops," shouted Abubakar Shekau, whose Islamist insurgency has terrorized northern Nigeria and recently drawn search-and-rescue advisers from the U.S. and other countries....